Which of the following numbers is a factor of 63? ${2,8,9,10,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $63$ by each of our answer choices. $63 \div 2 = 31\text{ R }1$ $63 \div 8 = 7\text{ R }7$ $63 \div 9 = 7$ $63 \div 10 = 6\text{ R }3$ $63 \div 14 = 4\text{ R }7$ The only answer choice that divides into $63$ with no remainder is $9$ $ 7$ $9$ $63$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $63$ $63 = 3\times3\times7 9 = 3\times3$ Therefore the only factor of $63$ out of our choices is $9$. We can say that $63$ is divisible by $9$.